Method for Acquiring and Modelling with a Lidar Sensor an Incident Wind Field

ABSTRACT

The invention relates to a method for detecting aberrant values of an incident wind field in a space located upstream of a lidar sensor. The method comprises acquiring and modelling a measurement rws(k) with the lidar sensor of an incident wind field, by estimating a median mr(k) and a mean absolute deviation dr(k) in real time of measurements of the incident wind field and detecting aberrant values in real time using the estimated median mr(k) and the mean absolute deviation dr(k).

CROSS REFERENCE TO RELATED APPLICATIONS

Reference is made French Application No. 18/71.844 filed Nov. 26, 2018,which is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to the field of lidar (light detection andranging) sensors used as remote-sensing means for measuring wind speed.It also relates to the field of wind turbines equipped with lidarsensors, and to the control of such wind turbines.

Description of the Prior Art

The detection of aberrant values is ubiquitous in many data-processingtasks, covering a wide range of fields such as signal processing,industrial control, etc. A good definition of an aberrant value is ameasurement that differs so greatly from the other measurements thatthere is suspicion that it is caused by a different mechanism.

In the field of wind power, over the last few years, the detection andobservation of light using lidar has been recognized as a reliable andfeasible remote-sensing technology for measuring and predicting windspeed.

Specifically, recent progress in lidar technology has facilitated thedeployment of lidar for real-time control applications. Lidar deliversmeasurements that characterize the upstream wind flux with high spatialand temporal resolutions. Patent application FR 3013777 corresponding toUS published application 2015/145253 describes such an application. Withlidar, measurements that differ substantially from the normal range ofthe detected data are considered to be aberrant values. These aberrantvalues may be caused by sensor errors or data-transmission errors.

Measurement-dependent wind predictions depend greatly on the quality ofthe lidar measurements. As the measurement data of the lidar inevitablycontains aberrant data, including erroneous data generated for reasonssuch as apparatus malfunctions or valid data representing extraordinarysituations such as unfavourable meteorological conditions, thepredictions are impacted and often not optimal.

In addition, the reconstruction of the wind field comprises estimatingthe wind speed and the confidence interval, and, in general, both relyon the quality of the lidar measurement.

Therefore, the detection of aberrant values gives beneficial insightrequired to make the application of lidar data workable.

Motivated by the desire to collect more useful information from lidardata, the invention mitigates the aforementioned drawbacks and providesa method allowing aberrant values to be removed in real time. Theapproach has been validated for lidar systems mounted on nacelles, withreal measurement data.

SUMMARY OF THE INVENTION

A first aspect of the invention relates to a method for detectingaberrant values of an incident wind field in a space located upstream ofa lidar sensor. The method comprises:

a) acquiring and modelling measurement rws(k) with the lidar sensor ofan incident wind field;b) estimating a median mr(k) and the mean absolute deviation dr(k) inreal time of the measurements of the incident wind field; andc) detecting aberrant values in real time using the estimated medianmr(k) and the mean absolute deviation dr(k), the detecting step beingcarried out with a formula:

|rws(k)−m _(r)(k)|≤σd _(r)(k) where σ is a positive scalar.

According to one aspect of the invention, the mean absolute deviationdr(k) in real time of the incident wind field is given by a formula:

$d_{r} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\; {{x_{i} - {m(X)}}}}}$

According to one implementation of the invention, the method comprises astep of reconstructing the measurement of the lidar sensor, by removingthe detected aberrant values from the modelled measurement rws(k).

Thus, a clean measurement signal without aberrant values is obtained.

According to one aspect of the invention, the method for acquiring andmodelling with a lidar sensor an incident wind field in a space locatedupstream of the lidar sensor comprises the following steps:

a) generating a mesh of the space located upstream of the lidar sensor,in which the mesh of the space is generated using a set of discretepoints positioned in a predefined three-dimensional grid comprising aset of cells composed of estimation points and of measurement points.

The mesh-generation step allows the space upstream of the lidar sensorto be discretized (or sampled) to form a three-dimensional grid composedof discrete points, and it is possible for these various discrete pointsto be made to coincide either with measurement points or with estimationpoints required by the modelling method. It furthermore allows themeasurement and estimation points to be positioned relative to oneanother and the distances separating all of these discrete points to beknown.

b) measuring the amplitude and direction of the wind at the variousmeasurement points located in the upstream space and positioned at atleast two different distances from the lidar sensor, along at leastthree measurement axes,

The measurements carried out in this step provide sufficient reliableinitial data to use an algorithm for estimating the amplitude and thedirection of the wind at the estimation points.

c) estimating the amplitude and the direction of the wind at any time atall of the estimation points, the estimation being carried out byoptimization, using a weighted recursive least-squares method, of a costfunction J that uses at least the data of the measured points, spatialwind-speed coherence data, temporal wind-speed coherence data, and dataqualifying the quality of the measurements carried out at themeasurement points.

Accounting for these various parameters in a cost function to beoptimized provides an estimation of the amplitude and of the directionof the wind at each estimation point of the mesh to be achieved.

d) reconstructing, in real time and in a defined coordinate system, theincident wind field in three dimensions (3D) from the wind amplitudesand directions estimated and measured for each point.

This step allows, in 3D, in the volume sampled by the three-dimensionalgrid, the reconstruction of incident wind field. In this step, a historyof the lidar measurements is generated, which allows the past states ofthe wind field to be known. This history is incorporated into thesynthesis of the current and future estimations of the 3D wind field,which allows reconstruction in real time.

The advantage of using an optimization approach, using a recursive formof the weighted least squares technique, makes possible determination ofa complete image in three dimensions (3D) of the incident windpropagating through the space located upstream of the lidar sensor.

According to one aspect of the invention, the measurement m of theamplitude and of the direction of the wind at a measurement point isgiven by a relationship of the form:

m _(j,x)(k)=a _(j) v _(j,x)(k)+b _(j) v _(j,y)(k)+c _(j) v _(j,z)(k)

where v_(j,x)(k), v_(j,y)(k), v_(j,z)(k) are wind-speed values projectedinto a coordinate system x, y, z at an initial time (k), and a_(j),b_(j), c_(j) with j=0, 1, 2, 3, 4 are measurement coefficients, whichare given by

$\left\{ {\begin{matrix}{{{a_{j} = {\cos \left( \theta_{j} \right)}},}\mspace{79mu}} \\{{b_{j} = {{\sin \left( \theta_{j} \right)}\mspace{14mu} {\cos \left( \phi_{j} \right)}}},} \\{{c_{j} = {{\sin \left( \theta_{j} \right)}\mspace{14mu} {\sin \left( \phi_{j} \right)}}}\mspace{11mu}}\end{matrix}\quad} \right.$

where θj, φj are, respectively, the zenith and the azimuth of themeasurement axis in a spherical coordinate system.

In this way the wind vector, at each sampled time, for all of the pointsof the space, is composed of three components that will allow thecomplete image to be determined in three dimensions. Furthermore, thesemeasurement coefficients are dependent only on the angles of the beamand are not dependent on the measurement distances, this facilitatingthe computational programming of the cost function J.

According to one aspect of the invention, the cost function J at anytime (t) is written in the following form:

${J(t)} = {{\left( {{\omega (0)} - {\hat{\omega}(0)}} \right)^{T}{P_{0}^{- 1}\left( {{\omega (0)} - {\hat{\omega}(0)}} \right)}} + {\sum\limits_{j = 1}^{t}\; {\left( {{\omega (j)} - {\omega \left( {j - 1} \right)}} \right)^{T}{Q^{- 1}\left( {{\omega (j)} - {\omega \left( {j - 1} \right)}} \right)}}} + {\sum\limits_{j = 1}^{t}\; {{\omega (j)}^{T}C_{s}^{T}R_{s}^{- 1}C_{s}{\omega (j)}}} + {\sum\limits_{j = 1}^{t}\; {\left( {{C_{m}{\omega (j)}} - m_{m}} \right)^{T}{R_{m}^{- 1}\left( {{C_{m}{\omega (j)}} - {m_{m}(j)}} \right)}}}}$

where ω is an ordered vector composed of all the components of the speedat the points of the space at which the wind is estimated, {circumflexover (ω)}(0) is the estimation of the wind speed at the time 0, P₀, Q,R_(s) and R_(m) are weighting matrices of suitable size, and C_(s),C_(m) are matrices that take into account the wind speed and themeasurement noise.

Using such a cost function, it is possible to estimate the wind speed atan estimation point. Furthermore, such a function makes it possible toachieve a clear interpretation of the weighting matrices P_(o), Q, R_(s)and R_(m).

According to one aspect of the invention, the measurements of theamplitude and direction of the wind at the various measurement pointsare carried out at a sampling rate of at least 0.25 Hz. The use of sucha sampling frequency range results in a plurality of measurements beingobtained simultaneously on a given measurement axis, these measurementsnonetheless being reliable and precise.

According to one aspect of the invention, the measurements of theamplitude and direction of the wind at the various measurement pointsare carried out at at least two different distances along themeasurement axis. Taking measurements at at least two distances allows athree-dimensional volume to be defined that is sufficient to encompassthe blades of a wind turbine, as will be described below.

According to one aspect of the invention, the measurements of theamplitude and direction of the wind are taken along at least threemeasurement axes. Employing at least three measurement axes makespossible generation of a fine mesh of the upstream space which providesa quantity of measurements sufficient for perform the step of estimatingthe wind speed to be obtained.

According to one aspect of the invention, the spatial coherence of thewind speed along the x, y and z axes of a Cartesian coordinate system isestimated using a formula:

C_(s)ω ≈ 0 $C_{s} = \begin{bmatrix}C_{l} \\C_{t} \\C_{v}\end{bmatrix}$ with :

-   -   C_(l) characterizing the variation in the wind speed for an        estimation domain along the longitudinal axis x;    -   C_(t) characterizing the variation in the wind speed for an        estimation domain along the lateral axis y;    -   C_(v) characterizing the variation in the wind speed for an        estimation domain along the vertical axis z.

The effect of such a characterization makes possible coding such afunction computationally.

According to one aspect of the invention, the spatial coherence of thewind speed along the x, y and z axes of the Cartesian coordinate systemis estimated under the following assumptions:

-   -   The variation in the wind speed along the longitudinal axis x is        small and the partial derivative dv_(x)/dx is relatively small        along the longitudinal axis,    -   the wind changes without discontinuity along the lateral axis y        and the partial derivative dv_(x)/dy is small along the lateral        axis y,    -   the wind changes along the vertical axis z according to a power        law, which is given by the formula:

$v_{l} = {v_{lr}\left( \frac{z}{z_{r}} \right)}^{\alpha}$

where α is an exponent of the power law, v_(l) is the longitudinal windat an altitude z above the ground, and z_(r) a reference altitude.Such assumptions are realistic and allow wind-speed estimations that arereliable and precise to be obtained.

According to one aspect of the invention, the quality of themeasurements carried out by the lidar is represented using a model ofthe form:

C _(m) ω=m _(m)+∈_(m)

where E_(m) describes the measurement noise.

This type of model allows inaccuracies in the lidar measurements to betaken into account.

According to one aspect of the invention, the estimation of theamplitudes and of the directions of the wind field at a time (t) at allof the estimation points is given by the following formula:

ω(t)=ω(t−1)+K(y(t)−Cω(t−1))

The advantage of the above formula is that it links the wind-speedestimations over time for the estimation points.

The invention also relates to a computer-program product that comprisescode instructions which implement the steps of the method for detectingaberrant values described above. The program is executed by a processingunit of the lidar.

The invention also relates to a lidar sensor that comprises in memorythe code instructions of a computer-program product such as describedabove and which is arranged to execute such a computer-program product.

In this way, a lidar sensor executing such a computer-program productreturns reliable information on an incident wind field in threedimensions and in real time.

One subject of the invention also relates to a wind turbine thatcomprises a lidar sensor such as described above.

According to one aspect of the invention, the lidar sensor is placed onthe nacelle of the wind turbine.

Lastly, the invention also relates to a method at least one ofcontrolling and monitoring a wind turbine equipped with a lidar sensorand a programmable logic controller. The method comprising followingsteps:

-   -   a) generating an anticipatory control strategy for controlling        the wind turbine and exploiting the detection of aberrant values        achieved via the reconstruction of the incident wind field in        three dimensions and in real time,    -   b) controlling, by using the generated control strategy, by        controlling an angle of the blades or orientation of the        nacelle.

Having a sufficiently robust and precise information regards the stateof the incident wind approaching the rotor allows a new approach tocontrol including integrating a dynamic and preventive pre-positioningterm. Furthermore, the ability to reconstruct, on-line, in real time, anincident wind field approaching the rotor plane opens up many potentialapplications such as quantification of the misalignment of the windturbine, a power curve, a transfer function of the nacelle, detection ofgusts, monitoring and diagnosis of load and the risk of fatigue,optimization of preventive maintenance, analysis of the resource andoptimization of production. This allows the efficiency of a wind turbineto be increased, the cost of maintenance to be decreased, the lifetimeof components to be increased and investment costs to be decreased bydesign optimization.

DESCRIPTION OF THE DRAWINGS

Other features and advantages of the method according to the inventionwill become apparent on reading the description below of one nonlimitingexample embodiment, with reference to the appended Figs., which aredescribed below.

FIG. 1 illustrates lidar measurements for one beam and for one day.

FIG. 2 illustrates lidar measurements after aberrant values have beenremoved for one beam and for one day.

FIG. 3 illustrates a wind turbine equipped with a lidar sensor accordingto the invention.

FIG. 4 illustrates the steps of the method for acquiring and modellingwith the lidar sensor according to the invention.

FIG. 5 is a face-on view of the mesh of the space according to theinvention.

FIG. 6 is a perspective view of the mesh of the space according to theinvention.

FIG. 7 illustrates a wind field in 3D reconstructed from the lidarmeasurements in one particular case.

FIG. 8 illustrates the steps of the method for controlling the windturbine according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

Notations

In the description, the following notations are used:

-   -   x, y, z are directions of the three-dimensional coordinate        system, with z the vertical axis and x the principal direction        of the wind.    -   Θ and φ are angles of orientation of the lidar sensor. These        angles are shown in [FIG. 1] with the angle θ being the angle        made by the projection of the measurement axis of the lidar in        the plane (y, z), and φ is the angle made by the projection of        the measurement axis of the lidar in a plane formed by the axis        x and the projection of the measurement axis of the lidar in the        plane (y, z).    -   m(t) is measurement of the lidar sensor at a measurement point.    -   V_(j,x)(k), v_(j,y)(k), v_(j,z)(k) are projections of the wind        speed on x, y, z.    -   ω is the ordered vector composed of all the components of the        wind speed at the points of the space at which the wind is        estimated on the axes x, y and z of the three-dimensional        coordinate system.    -   {circumflex over (ω)}(t) is the estimation of ω(t) at the time        t.    -   P(t) is the auxiliary matrix array that is variable over time,        and which may be obtained at the time t.    -   P₀, Q, R_(s) and R_(m) are weighting matrices of suitable size.        is a positive scalar.    -   Rp is a vector.    -   mr(k) is a median.

In the rest of the description, the term “lidar” is used to designate alidar sensor.

A method for detecting aberrant values in real time is provided, whichis based on an on-line estimation of the median and the mean absolutedeviation. The method has been validated using real lidar-measurementdata, showing that aberrant values may be detected and must be removedfrom the lidar measurements.

A 5-beam pulsed nacelle lidar as shown in [FIG. 3] measures thecomponent of the wind speed that corresponds to the wind speed projectedin the direction of the laser beam, namely the beam b0, then the beamb1, the beam b2, the beam b3, and lastly beam b4. An advantageousfeature of the lidar is that it is able to measure the projection of thewind speed at a plurality of distances along each beam, for example atdistances from 50 to 200 m, at a sampling rate of 4 Hz. At each samplingtime, only the measurements of one beam may be obtained.

As shown in [FIG. 1], which shows the lidar measurements for one beamand for one day in the case where the detecting method was not used, itmay be seen that the lidar does not deliver measurements all the time(specifically, this effect may be observed during the time intervalbetween [6×10⁴:7×10⁴]), and that, at most times, the lidar measurementssignificantly deviate from the normal range. These measurements areconsidered to be aberrant values.

As previously indicated, the invention detects and removes aberrantvalues from the lidar measurements.

To do this, a first step of the method for detecting aberrant values inreal time acquires and models measurement rws(k) with the lidar sensorof an incident wind field. This step will be described in more detail inthe rest of the description.

A second step carried out with the lidar estimates the median and themean absolute deviation in real time of the lidar measurements that willsubsequently be used to detect aberrant values.

In statistics, the median is the value separating the lower half fromthe upper half of a data sample. For a dataset, it may be considered tobe the middle value. For example, in a dataset {1, 3, 3, 6, 7, 8, 9},the median is 6, the fourth highest and the fourth lowest number of thesample. The main advantage of the median in the description of data,with respect to the mean, is that it is not distorted by extremely highor extremely low values, this making it obtaining a better value of thetypical value. In other words, the median is much more robust withrespect to aberrant values than the mean. In the case of symmetric data,the mean and the median are equal.

The invention comprises a procedure for computing the median of the 2nm+1 lidar-measurement data.

In the following example, which is illustrated in [FIGS. 1 and 3], onlymeasurement with one beam for one distance is considered. However, theapproach is directly extendable to all the beams and to all thedistances.

The detecting method comprises an algorithm that estimates the median inreal time. The data used are listed below:

-   -   Parameter: Number of data 2 nm+1    -   Input: Lidar measurements rws(k)    -   Output: Median mr(k)    -   Initialization: j=1    -   The algorithm operates in the following way at each time k:        1. If j≤2 nm+1    -   a) rp(j)=rws(k)    -   b) j=j+1    -   c) Go to 1.

2. Otherwise:

-   -   a) rp(1: 2 nm)=rp(2: 2 nm+1)    -   b) rp(2 nm+1)=rws(k)    -   c) Sort the vector rp into increasing order.        3. The median mr(k) is computed as mr(k)=rp(nm).        This algorithm only requires storage and sorting operations,        which are extremely simple.

For the problem of detecting aberrant values, estimating the meanabsolute deviation is necessary. In mathematics, the mean absolutedeviation of a dataset is the mean of the absolute deviations withrespect to a central point, that is for a set X={x1, x2, . . . , xn},the mean absolute deviation is computed as:

$d_{r} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\; {{x_{i} - {m(X)}}}}}$

The central point m(X) may be the mean, the median or the mode. For thesake of robustness with respect to the aberrant values, the median mr(k)is chosen as m(X).

The mean absolute deviation is a measurement used to quantify the amountof variation or dispersion in a set of data values. A low absolutedeviation indicates that the data points have a tendency to be close tothe central point of the set, whereas a high absolute deviationindicates that the data points are distributed over a wider range ofvalues. The main advantage of the mean absolute deviation with respectto the standard deviation is that it is much more robust than thestandard deviation with respect to aberrant values.

Below, an algorithm for computing the mean absolute deviation of thelidar data np. measured beforehand is provided. For greater simplicity,only measurement with one beam for one distance is considered.

To this end, the data used by the algorithm are listed below:

-   -   Parameter: Number of data np    -   Input: Lidar measurement rws(k)    -   Output: Mean absolute deviation dr(k)    -   Initialization: j=1    -   At each time k:

1. If j np

-   -   a) dp(j)=rws(k)    -   b) j=j+1    -   c) Go to 1.

2. Otherwise

-   -   a) dp(1: np−1)=dp(1:np)    -   b) dp(np)=rws(k)        3. The algorithm for estimating the median in real time is used        to estimate the median mr(k).        4. The mean absolute deviation dr(k) is computed as:

${d_{r}(k)} = {\frac{1}{n_{p}}{\sum\limits_{i = 1}^{n_{p}}\; {{{d_{p}(i)} - {m_{r}(k)}}}}}$

In this section, a procedure for detecting the aberrant values in realtime using the estimated median mr(k) and the estimated mean absolutedeviation dr(k) is used. It will be recalled that the median may beconsidered to be the middle value, by virtue of which the mean absolutedeviation dr(k) quantifies the amount of variation in or a dispersion ofa set of data values.

In order to detect the aberrant values, it is assumed that the lidarmeasurements rws(k) cannot change so rapidly, that is the difference|rws(k)−mr(k)| is small. More precisely, it is assumed that:

|rws(k)−m _(r)(k)|≤σd _(r)(k)

where σ is a positive scalar.

In this way, all the lidar measurements that do not satisfy thepreceding equation are considered to be aberrant values.

Thus the method for detecting aberrant values is comprised in analgorithm for detecting aberrant values that may be summarized asfollows:

-   -   The parameters of this algorithm are:    -   Input: Lidar measurement rws(k)    -   Output: Detect whether rws(k) is an aberrant value or not.    -   Thus, at each time k, the algorithm performs the following        operations:        -   1. Using the algorithm to estimate the median mr(k).        -   2. Using the algorithm to estimate the mean absolute            deviation dr(k).        -   3. If |rws(k)−mr(k)|σdr(k), then rws(k) is not an aberrant            value.        -   It may be used in a wind-field reconstruction algorithm.        -   4. Otherwise: rws(k) is an aberrant value.

According to one implementation of the invention, the method comprises astep of reconstructing the measurement of the lidar sensor, by removingthe detected aberrant values from the modelled measurement rws(k).

Thus, a clean measurement signal without aberrant values is obtained.

FIG. 4 shows the various steps of the acquiring and modelling methodaccording to one embodiment of the invention: Other variant embodimentsof the acquiring and modelling process known to those skilled in the artare suitable for the method according to the invention.

-   -   1. Generating a mesh (MA) of the space located upstream of the        lidar sensor, the mesh comprising estimation points (PE) and        measurement points (PM).    -   2. Measuring (MES) the amplitude and the direction of the wind        at the various measurement points (PM).    -   3. Estimating (EST) the amplitude and the direction of the wind        at any time (t) for all of the estimation points (PE).    -   4. Reconstructing (MOD 3D) the incident wind field in three        dimensions (3D) and in real time at all of the discrete points.

FIG. 3 shows a wind turbine 1 equipped with a lidar sensor 2. The lidarsensor 2 is used to measure the wind speed at a given distance and at ameasurement point PM. Knowledge in advance of the wind measurement inprinciple makes it possible to generate a lot of information.

There are a plurality of types of lidar sensors, for example scannedlidar sensors, continuous lidar sensors or pulsed lidar sensors. In thecontext of the invention, a pulsed lidar is preferably used. However,other lidar technologies may be used while remaining within the scope ofthe invention. As may be seen in [FIG. 1], which is one exampleembodiment, the lidar used comprises 5 beams or measurement axes (b0,b1, b2, b3, b4). Nonlimitingly, the acquiring and modelling method alsooperates with a lidar comprising three or more beams. The pulsed 5-beamlidar sensor is mounted on a nacelle 3 of a wind turbine 1.

Conventionally, a wind turbine 1 allows the kinetic energy of the windto be converted into electrical or mechanical energy. For the conversionof the wind into electrical energy, the wind turbine is composed of thefollowing elements:

-   -   a mast 4 allowing a rotor (not shown) to be placed at a        sufficient height to allow it to move (required for        horizontal-axis wind turbines) or this rotor to be placed at a        height allowing it to be driven by a wind that is stronger and        more regular than at the level of the ground 6. The mast 4        generally houses some of the electrical and electronic        components (modulator, command unit, multiplier, generator,        etc.);    -   a nacelle 3 mounted at the top of the mast 4, housing        mechanical, pneumatic components and certain electrical and        electronic components (not shown) required for the operation of        the machine. The nacelle 3 may turn to orient the machine in the        correct direction;    -   the rotor, fastened to the nacelle, comprising a plurality of        blades 7 (in general three) and the nose cone of the wind        turbine. The rotor is driven by the energy of the wind, it is        connected by a mechanical shaft directly or indirectly (via a        gearbox and mechanical shaft system) to an electrical machine        (electrical generator, etc.) (not shown) that converts the        harvested energy into electrical energy. The rotor is        potentially equipped with control systems such as variable-angle        blades or aerodynamic brakes;    -   a transmission, composed of two axles (mechanical shaft of the        rotor and mechanical shaft of the electrical machine) that are        connected via a transmission (gearbox) (not shown).

In the description given below, the described acquiring and modellingmethod is theoretical and works independently of the wind turbine 1.However, the various examples and developments are given in the case ofa lidar mounted on the nacelle 3 of the wind turbine 1 and hence thevarious steps of the acquiring and modelling method that are shown inFIG. 4 are carried out at a certain altitude with respect to the ground6.

In this part, the various steps of the acquiring and modelling methodaccording to the invention are described:

1. Generating a Mesh (MA) of the Space Located Upstream of the LidarSensor

In this first step, the space upstream of the lidar sensor is definedinto a mesh, as shown in [FIGS. 3, 5 and 6]. In this step, a coordinatesystem in which the lidar performs the measurements is defined. Thedefined coordinate system is the direct system of axes illustrated in[FIGS. 3 and 5]. The x-y origins of this system are at the level of theposition of the lidar on the nacelle 3, and the z origin is at the levelof the ground 6.

The x-axis points horizontally in the direction of the wind, the z-axispoints vertically upward and the y-axis is perpendicular in order toform a direct three-dimensional coordinate system (in accordance withthe right-hand rule).

In this step, the generation of the mesh of the space comprisesgenerating a set of discrete points placed upstream and that define athree-dimensional grid. For each given distance x, the y-z plane isdivided into cells without overlap as shown in [FIG. 5]. The meshcomprises measurement points (PM) and estimation points (PE) at whichthe wind speed is measured and estimated, respectively.

In relation to this mesh of the space, underlying variables, calledoptimization variables, which are necessary for the estimating stepdescribed below, are also defined. In order to allow a clever andeffective implementation of the optimization algorithm described below,all the optimization variables are assembled into an ordered vector,which is denoted ω. The determined order of these optimization variablesis an engineering element that is crucial to the feasibility andperformance of a coding algorithm of this method.

A vector ω is defined for each point of the discretized space, and it iscomposed of all the components v_(x) of the points (PE) of the spacewhere the wind is estimated, followed respectively by the componentsv_(y) and v_(z). The estimation of the wind speed at n points involvesconstructing a vector ω of 3n size, with w₁ to w_(n) containing all thev_(x), w_(n+1) to w_(2n) containing all the v_(y), and w_(2n+1) tow_(3n) containing all the v_(z).

The following example is given for the components v_(x) of the windspeed, but it will be understood that the method is identical for v_(y)and v_(z). As was done in the initial step, and as shown in [FIG. 5],the space is discretized in x, y and z with n_(x) points in x, n_(y)points in y and n_(z) points in z.

In this configuration:

n=n _(x) n _(y) n _(z)

The component v_(x) of the wind speed the coordinates of which is(x_(i), y_(j), z_(k)) is defined by v_(i,j,k).The index l of w_(l), at which the corresponding estimation is located,is obtained thus:

l=(n _(x) −i)n _(y) n _(z)+(k−1)n _(y) +j

For example, if i=n_(x), k=1 and j=1, then

l=(n _(x) −i)n _(y) n _(z)+(k−1)n _(y) +j=1

This corresponds to the top left corner of the estimation domain, at thedistance most upstream from the rotor plane, as illustrated in [FIG. 6].

2. Measuring (MES) the Amplitude and the Direction of the Wind at theVarious Measurement Points

In a second step, the lidar sensor carries out a measurement m(t)relating to the wind speed at a measurement point (PM) located upstreamof the wind turbine 1. This measurement m(t) corresponds to the signalreceived by the sensor coming from the measurement point (PM) inresponse to the signal emitted by the lidar sensor. Specifically, viainterferometry and the Doppler effect, a portion of the laser signalemitted by the lidar sensor is reflected by air molecules at themeasurement point and also by aerosols (dust and micro-particles insuspension). The measurement point is defined by the characteristics ofthe lidar sensor, in particular its focal length, and by itsorientation. This measurement, which is dependent on the wind speed, isa time and depends on the orientation of the lidar sensor.

For the study of a case of a pulsed lidar, the measurements are obtainedsuccessively on the mesh defined in the preceding step, starting withthe longitudinal beam b0, then the oblique beam b1, up to the beam b4.One advantageous feature of this system is that it allows the projectionof the wind speed to be measured at a plurality of distances,simultaneously, for a given beam. It is thus possible to for exampleobtain 10 successive distances between 50 m and 400 m, at a samplingrate of 0.25 Hz or of 1 Hz. It is of course possible to limit themeasurements to two measurements, which are sufficient to reconstruct athree-dimensional model. At each sampling time, only the measurements ofthe selected current beam are refreshed.

In one particular case, according to [FIG. 6], the measurements are madeat seven distances and in particular at x=[50 80 120 160 200 240 280] mfor the five beams. Thus, for each given x, the y-z plane is dividedinto cells as follows:

-   -   Four first points (PM) corresponding to the y-z coordinates of        the measurement points for the beams 1, 2, 3, 4 at the distance        x=280 m.    -   Four second points (PM1) corresponding to the y-z coordinates of        the measurement points for the beams 1, 2, 3, 4 at the distance        x=240 m.    -   Four third points (PM2) corresponding to the y-z coordinates of        the measurement points for the beams 1, 2, 3, 4 at the distance        x=200 m.    -   Four fourth points (PM3) corresponding to the y-z coordinates of        the measurement points for the beams 1, 2, 3, 4 at the distance        x=160 m.    -   Four fifth points (PM4) corresponding to the y-z coordinates of        the measurement points for the beams 1, 2, 3, 4 at the distance        x=120 m.    -   Four sixth points (PM5) corresponding to the y-z coordinates of        the measurement points for the beams 1, 2, 3, 4 at the distance        x=80 m.    -   Four seventh points (PM6) corresponding to the y-z coordinates        of the measurement points for the beams 1, 2, 3, 4 at the        distance x=50 m.    -   The central point (PM7) corresponds to the y-z coordinates of        the measurement points for beam 0 for all the distances.

The lidar measurements m(k) for the beams j=0, 1, 2, 3, 4 at thedistance x metres, and at the time k are given by the formula mj, x(k),with j=0, 1, 2, 3, 4.

For example, m_(0,50)(1) is the lidar measurement for the beam j=0 atthe distance x=50 meters and at the instant of time k=1. In the contextof the invention, the lidar measurement is then given by a formula ofthe type:

m _(j,x)(k)=a _(j) v _(j,x)(k)+b _(j) v _(j,y)(k)+c _(j) v _(j,z)(k)

-   -   where v_(j,x)(k), v_(j,y)(k), v_(j,z)(k) are wind-speed values        projected into a given coordinate system at the initial time        (k), and a_(j), b_(j), c_(j), with j=0, 1, 2, 3, 4 are        measurement coefficients, which are given by,

$\left\{ {\begin{matrix}{{{a_{j} = {\cos \left( \theta_{j} \right)}},}\mspace{79mu}} \\{{b_{j} = {{\sin \left( \theta_{j} \right)}\mspace{14mu} {\cos \left( \phi_{j} \right)}}},} \\{{c_{j} = {{\sin \left( \theta_{j} \right)}\mspace{14mu} {\sin \left( \phi_{j} \right)}}}\mspace{11mu}}\end{matrix}\quad} \right.$

-   -   where θj, φj, with j=0, 1, 2, 3, 4 are the zenith and the        azimuth of the measurement axis in a spherical coordinate        system, respectively.

The advantage of defining the lidar measurement equation in thecoordinate system defined above, with the selected choice of spatialdiscretization, is that it may be used directly, since the coordinatesof the measurement point coincide with one particular point of thediscretized space.

3. Estimating (EST) the amplitude and the direction of the wind at anytime (t) at all of the discrete points

This step obtains a value of the wind at the estimation points (PE) ofthe mesh.

To this end, the estimation is carried out by use of the optimization,using a weighted recursive least-squares method, of a cost function thatuses the measured lidar data m(k), but also spatial wind-speed coherencedata, temporal wind-speed variation data, and data qualifying thequality of the lidar measurements m(k). This is explained below.

3.1 Spatial Differences

These subsections define the spatial wind coherence data used in thecontext of the invention and more particularly in the context of a lidarmounted on the nacelle 3 of a wind turbine 1.

In this step, the components of the wind speed on the axes x, y and z ofthe coordinate system defined above are considered.

In this estimating step, it is assumed that the wind speed changesrelatively little in the space, and that the wind has a high spatialcoherence in a small volume of the space. The following description isgiven here for the components v_(x), that is for the first n variablesof w, with an estimation domain shown in [FIG. 6] (the approach issimilar for the components v_(y) and v_(i)), and settingn_(x)=n_(y)=n_(z)=3.

3.1.1 Longitudinal Difference

The longitudinal difference corresponds to the change in v_(x) along thex-axis and it changes smoothly according to the invention. In this case,the partial derivative dv_(x)/dx is relatively small. In other words,

$\left\{ {\begin{matrix}{{{\omega_{1} - \omega_{10}} \approx 0}\mspace{11mu}} \\{{{\omega_{2} - \omega_{11}} \approx 0}\mspace{11mu}} \\{\vdots \mspace{140mu}} \\{{\omega_{18} - \omega_{27}} \approx 0}\end{matrix}\quad} \right.$

The preceding equation may be written in a compact vector form as:

C_(xl)ω ≈ 0 where $C_{xl} = \begin{bmatrix}{+ 1} & 0 & \ldots & 0 & {- 1} & 0 & \ldots & 0 \\0 & {+ 1} & \ldots & 0 & 0 & {- 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {+ 1} & 0 & 0 & \ldots & {- 1}\end{bmatrix}$

It will be noted that each row of C₄ contains one +1 and one −1.Analogously, it is possible to compute the variation in v_(y) and v_(z)along the longitudinal axis as:

$\left\{ {\begin{matrix}{{{C_{yl}\omega} \approx 0},} \\{{{C_{zl}\omega} \approx 0}\;}\end{matrix}\quad} \right.$

where C_(yl), C_(zl), are matrices of coefficients that contain only one+1 and one −1 in each row.

Defining:

$C_{l} = \begin{bmatrix}C_{xl} \\C_{yl} \\C_{zl}\end{bmatrix}$

the following equation is obtained:

C _(l)ω≈0

which characterizes the variation in the wind speed for the estimationdomain along the longitudinal axis.

3.1.2 Lateral Difference

The lateral difference is the change in v_(x) along the y-axis.Analogously, since the wind changes without discontinuity, the partialderivative dv_(x)/dy is relatively small. In other words,

$\left\{ {\begin{matrix}{{{\omega_{1} - \omega_{2}} \approx 0}\mspace{14mu}} \\{{{\omega_{2} - \omega_{3}} \approx 0}\mspace{14mu}} \\{\vdots \mspace{140mu}} \\{{\omega_{26} - \omega_{27}} \approx 0}\end{matrix}\quad} \right.$

It is possible to write the preceding equation in a compact vector formas

C_(xl)ω ≈ 0 where $C_{xl} = \begin{bmatrix}{+ 1} & {- 1} & 0 & \ldots & 0 & 0 & 0 & \ldots & 0 & 0 \\0 & {+ 1} & {- 1} & \ldots & 0 & 0 & 0 & \ldots & 0 & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\0 & 0 & 0 & \ldots & 0 & 0 & 0 & \ldots & {+ 1} & {- 1}\end{bmatrix}$

Each row of C_(xt) contains one +1 and one −1.Analogously, the variation in v_(y) and v_(z) along the lateral axis maybe computed as,

$\left\{ {\begin{matrix}{{{C_{yt}\omega} \approx 0},} \\{{{C_{zt}\omega} \approx 0}\;}\end{matrix}\quad} \right.$

where C_(yr), C_(zt) are matrices of coefficients that contain only one+1 and one −1 in each row.

Defining:

$C_{t} = \begin{bmatrix}C_{xt} \\C_{yt} \\C_{zt}\end{bmatrix}$

It is clear that the equation:

C _(t)ω≈0

characterizes the variation in the wind speed for the estimation domainalong the lateral axis.

3.1.3 Vertical Difference

The vertical profile of the wind speed is given by a power law, whichmakes possible obtaining a description of the wind-speed component v_(x)at various heights that is much more precise.

The vertical profile of the wind speed describes the variation in thelongitudinal wind speed as a function of the altitude relative to theground. The power law of the wind-speed profile is generally used toestimate the longitudinal wind speed v_(L) at an altitude z above theground, taking into account the longitudinal wind speed v_(lr) at areference altitude z_(r), using the equation,

$v_{l} = {v_{lr}\left( \frac{z}{z_{r}} \right)}^{\alpha}$

where alpha is the exponent of the power law, which is generallyspecified dependent on stability.The constant value alpha= 1/7 is commonly used, consistently with anassumption of a relatively low wind shear. However, it should be notedthat considering alpha to be constant amounts to ignoring the roughnessof the surface of the ground, interactions of the wind with potentialobstacles, and the stability of the atmosphere.Using this power law, the vertical difference of the wind is thus givenby:

$\left\{ {\begin{matrix}{{{\omega_{1} - {\left( \frac{z_{1}}{z_{4}} \right)^{\alpha}\omega_{4}}} \approx 0}\mspace{25mu}} \\{{{\omega_{2} - {\left( \frac{z_{2}}{z_{3}} \right)^{\alpha}\omega_{5}}} \approx 0}\mspace{25mu}} \\{\vdots \mspace{214mu}} \\{{\omega_{24} - {\left( \frac{z_{24}}{z_{27}} \right)^{\alpha}\omega_{27}}} \approx 0}\end{matrix}\quad} \right.$

where z_(j) is the height of w, and a is the exponent of the power law,which is assumed to be 1/7.It is possible to write the preceding equation in a compact vector formas:

     C_(xv)ω ≈ 0      where $C_{xv} = \begin{bmatrix}{+ 1} & 0 & 0 & {- \left( \frac{z_{1}}{z_{4}} \right)^{\alpha}} & 0 & 0 & \ldots & 0 & 0 & 0 & 0 \\0 & {+ 1} & 0 & 0 & {- \left( \frac{z_{2}}{z_{3}} \right)^{\alpha}} & 0 & \ldots & 0 & 0 & 0 & 0 \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots \\0 & 0 & 0 & 0 & 0 & 0 & \ldots & {+ 1} & 0 & 0 & {- \left( \frac{z_{24}}{z_{27}} \right)^{\alpha}}\end{bmatrix}$

Analogously, it is possible to quantify the variation in v_(y) and v_(z)along the vertical axis as:

$\left\{ {\begin{matrix}{{{C_{yv}\omega} \approx 0},} \\{{{C_{zv}\omega} \approx 0}\;}\end{matrix}\quad} \right.$

However, as the power law of the profile of the wind applies only to thelongitudinal wind speed, C_(yv) and C_(zv) contain only one +1 and one−1 in each row.

Defining:

$C_{v} = \begin{bmatrix}C_{xv} \\C_{yv} \\C_{zv}\end{bmatrix}$

The following equation is obtained:

C _(v)ω≈0

which characterizes the variation in the wind speed for the estimationdomain along the vertical axis.axisLastly, using

C _(l)ω≈0

and

C _(t)ω≈0

the following may be stated:

$\left\{ {\begin{matrix}{{{C_{l}\omega} \approx 0},} \\{{{C_{t}\omega} \approx 0},} \\{{{C_{v}\omega} \approx 0}\;}\end{matrix}\quad} \right.$

or equivalently,which is the equation that characterizes the total variation in windspeed along the x-, y- and z-axes.

With:

$C_{s} = \begin{bmatrix}C_{l} \\C_{t} \\C_{v}\end{bmatrix}$

3.2 Lidar Measurements

For the sake of the computation, it is important to rewrite themeasurement equation in the vector form of W. In the preceding exampleof a five-beam lidar and for seven measurements per beam, j=0, 1, 2, 3,4, and x=[50, 80, 120, 160, 200, 240, 280],

$\left\{ {\begin{matrix}{v_{j,x} = {{\left\lbrack {0\mspace{14mu} \ldots \mspace{14mu} 0\mspace{14mu} 1\mspace{14mu} 0\mspace{14mu} \ldots \mspace{14mu} 0} \right\rbrack \omega} = {C_{j,{xx}}\omega}}} \\{v_{j,y} = {{\left\lbrack {0\mspace{14mu} \ldots \mspace{14mu} 0\mspace{14mu} 1\mspace{14mu} 0\mspace{14mu} \ldots \mspace{14mu} 0} \right\rbrack \omega} = {C_{j,{xy}}\omega}}} \\{v_{j,z} = {{\left\lbrack {0\mspace{14mu} \ldots \mspace{14mu} 0\mspace{14mu} 1\mspace{14mu} 0\mspace{14mu} \ldots \mspace{14mu} 0} \right\rbrack \omega} = {V_{j,{xz}}\omega}}}\end{matrix}\quad} \right.$

In combination with:

m _(j,x)(k)=a _(j) v _(j,x)(k)+b _(j) v _(j,y)(k)+c _(j) v _(j,z)(k)

the following is obtained,

m_(j, x) = C_(j, x)ω where$C_{j,x} = {\left\lbrack {a_{j}\mspace{14mu} b_{j}\mspace{14mu} c_{j}} \right\rbrack \mspace{14mu}\begin{bmatrix}C_{j,{xx}} \\C_{j,{xy}} \\C_{j,{xz}}\end{bmatrix}}$

which may be rewritten in a compact vector form:

C_(m)ω = m_(m) where ${m_{m} = \begin{bmatrix}{m_{0,50}\mspace{11mu}} \\{m_{1,50}\mspace{11mu}} \\{\vdots \mspace{56mu}} \\m_{4,280}\end{bmatrix}},{C_{m} = \begin{bmatrix}{C_{0,50}\mspace{11mu}} \\{C_{1,50}\mspace{11mu}} \\{\vdots \mspace{56mu}} \\C_{4,280}\end{bmatrix}}$

In order to take into account measurement noise, a more realistic modelfor the lidar measurements may be introduced as follows,

C _(m) ω=m _(m)+∈_(m)

where ε_(m) describes the measurement noise.

3.3 Weighted recursive least-squares method

It is assumed that the wind speed changes little in the space, and overtime. Below, a method for taking into account this information in theoptimization approach is provided. {circumflex over (ω)}(0) is theestimation of the wind speed at the time 0. At each time, theoptimization problem is the following:

$\mspace{76mu} {\min\limits_{\omega {(t)}}\mspace{14mu} {J(t)}}$     with:${J(t)} = {{\left( {{\omega (0)} - {\hat{\omega}(0)}} \right)^{T}{P_{0}^{- 1}\left( {{\omega (0)} - {\hat{\omega}(0)}} \right)}} + {\sum\limits_{j = 1}^{t}\; {\left( {{\omega (j)} - {\omega \left( {j - 1} \right)}} \right)^{T}{Q^{- 1}\left( {{\omega (j)} - {\omega \left( {j - 1} \right)}} \right)}}} + {\sum\limits_{j = 1}^{t}\; {{\omega (j)}^{T}C_{s}^{T}R_{s}^{- 1}C_{s}{\omega (j)}}} + {\sum\limits_{j = 1}^{t}\; {\left( {{C_{m}{\omega (j)}} - m_{m}} \right)^{T}{R_{m}^{- 1}\left( {{C_{m}{\omega (j)}} - {m_{m}(j)}} \right)}}}}$

There are four terms in the preceding cost function.

-   -   The first term penalizes knowledge of the initial wind speed        ω(0).    -   The second term penalizes the variation in the wind speed over        time.    -   The third term penalizes the variation in the wind speed in the        space.    -   The fourth term penalizes the lidar measurement quality.

Using the preceding formula, it is possible to achieve a clearinterpretation of the weighting matrices P₀, Q, R_(s) and R_(m). Thus:

-   -   If the wind speed ω(t) at the time t=0 is well known, then        ω(0)={circumflex over (ω)}(0), then P₀ is small. Otherwise P₀ is        large.    -   If there are many variations in the wind speed over time, then Q        is large.        Otherwise Q is small.    -   If the wind speed changes rapidly, then R_(s) is large.        Otherwise R_(s) is small.    -   If there is a lot of noise in the lidar measurements, then R_(m)        is large. Otherwise, R_(m) is small.        Let the three following limiting cases be considered:    -   No information on the initial wind speed is available. Therefore        P₀ is very large. The term:

(ω(0)−{circumflex over (ω)}(0))^(T) P ₀ ⁻¹(ω(0)−{circumflex over(ω)}(0))

may thus be neglected in the cost function.There is no relationship between the wind speed at the time t and thewind speed at the time t−1. In this case, it is possible to choose Q tobe very large. The following term may be neglected:

$\sum\limits_{j = 1}^{t}\; {\left( {{\omega (j)} - {\omega \left( {j - 1} \right)}} \right)^{T}{Q^{- 1}\left( {{\omega (j)} - {\omega \left( {j - 1} \right)}} \right)}}$

-   -   The variation in the wind speed in the space is very small. In        this case, it is possible to make R_(s) very small. The        following term is important in the cost function:

$\sum\limits_{j = 1}^{t}\; {{\omega (j)}^{T}C_{s}^{T}R_{s}^{- 1}C_{s}{\omega (j)}}$

The following are defined:

${C = \begin{bmatrix}{C_{s}\;} \\C_{m}\end{bmatrix}},{R = \begin{bmatrix}R_{s} & 0 \\0 & R_{m}\end{bmatrix}}$

The weighted recursive least-squares method used to solve theoptimization problem is defined in the following way:

-   -   The optimization variables are initialized in the following way:

$\left\{ {\begin{matrix}{{{\omega (0)} = {\hat{\omega}(0)}},} \\{{{P(0)} = P_{0}}\mspace{25mu}}\end{matrix}\quad} \right.$

-   -   At each time t:        -   the following is defined:

${y(t)} = \begin{bmatrix}0 \\{y_{m}(t)}\end{bmatrix}$

Where 0 is a zero vector of suitable size.

-   -   An auxiliary matrix K is computed such that

K=(P(t−1)+Q)C(C ^(T)(P(t−1)+Q)C+R)⁻¹

-   -   The matrix P(t) is computed such that

P(t)=(I−KC)P(t−1)

where I is an identity matrix of suitable size.

-   -   The wind speed at the time t is then estimated thus:

ω(t)=ω(t−1)+K(y(t)−Cω(t−1))

4. Reconstruction of the Incident Wind Field in Three Dimensions (3D)and in Real Time

In this step, a processor integrated into the lidar sensor collects allof the wind-amplitude and wind-direction data measured and estimatedduring the preceding steps. The collection of these data is carried outin real time for each precedingly defined measurement and estimationpoint (PM, PE). Thus the lidar sensor is able to reconstruct all of thewind field incident on the lidar, as shown in [FIG. 7].

In [FIG. 7], a reconstructed wind field is shown for a time of 68seconds. The y-axis represents the altitude relative to the ground (inm) and the x-axes represent the distance to the nacelle (in m) andlateral positions relative to the lidar (in m).

The invention secondly relates to a method for at least one ofcontrolling and monitoring a wind turbine equipped with a lidar sensorsuch as described above and an associated programmable logic controller10 that comprises the following steps:

-   -   i) generating an anticipatory control strategy (CON) for        controlling the wind turbine 1 and exploiting the reconstruction        of the incident wind field in three dimensions and in real time        obtained using the method according to the invention;    -   ii) a control (PIL), incorporating the generated control        strategy, which in particular controls the angle of the blades 7        or the orientation of the nacelle 3.

FIG. 8 shows the overall operation of such a wind turbine 1. The windturbine 1 comprises to this end a lidar sensor 2 according to theinvention, and its processing unit, a computational device comprising asoftware solution for reconstructing in 3D the wind field, aprogrammable logic controller incorporating the control strategy and adevice for controlling at least one of the blades and the nacelle of thewind turbine. With reference to [FIG. 8], the invention applied to awind turbine works in the following way:

-   -   First, the lidar performs the step of acquiring and modelling        the incident wind field such as described above to reconstruct a        3D incident wind field (steps ME, MA, EST and MOD 3D in [FIG.        8]),    -   Second, the programmable logic controller 10 generates the        control strategy (CON) and controls (PIL) units of the wind        turbine 1 taking into account the generated control strategy.

This method according to the invention makes possible analysis inreal-time the incident wind or to detect gusts, power curves and thestrength of turbulence. This may possibly be applied to regulate ormonitor the wind turbine to obtain a better alignment of the windturbine, this leading to an optimization of production and aminimization of loads and of fatigue.

1.-18. (canceled)
 19. A method for detecting aberrant values of anincident wind field in a space located upstream of a lidar sensor,comprising: a) acquiring modelling measurement rws(k) with the lidarsensor of an incident wind field; b) estimating a median mr(k) and amean absolute deviation dr(k) in real time measurements of the incidentwind field; and c) detecting the aberrant values in real time using theestimated median mr(k) and the mean absolute deviation dr(k), with thedetecting step being carried out with a formula:|rws(k)−mr(k)|σdr(k) where σ is a positive scalar.
 20. The methodaccording to claim 19, wherein the mean absolute deviation dr in realtime of the incident wind field is given by a formula:$d_{r} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\; {{x_{i} - {m(X)}}}}}$wherein x is a coordinate in a defined system and m(X) is a centerpoint.
 21. The method according to claim 19, comprising reconstructingmeasurement of the lidar sensor, by removing the detected aberrantvalues from the modelled measurement rws(k).
 22. The method according toclaim 19, wherein acquiring and modelling with the lidar sensor anincident wind field in the space located upstream of the lidar sensorcomprises: a) generating a mesh of the space located upstream of thelidar sensor, the mesh of the space is generated using a set of discretepoints positioned in a predefined three-dimensional grid comprising aset of cells composed of estimation points and of measurement points; b)measuring the amplitude and direction of the wind at the various pointslocated in the upstream space and positioned at at least two differentdistances from the lidar sensor, along at least three measurement axes;c) estimating amplitude and direction of the wind at any time at allestimation points, the estimation being carried out by optimization,using a weighted recursive least-squares method, of a cost function thatuses at least data of the measurement points, spatial wind-speedcoherence data, temporal wind-speed coherence data, and data qualifyingthe quality of the measurements carried out at the measurement points;and d) reconstructing, in real time and in the defined coordinatesystem, the incident wind field in three dimensions from wind amplitudesand directions estimated and measured for each point of the mesh. 23.The method according to claim 22, wherein the measurement m of theamplitude and of the direction of the wind at a measurement pointm_(j,x)(k) is given by a relationship:m _(j,x)(k)=a _(j) v _(j,x)(k)+b _(j) v _(j,y)(k)+c _(j) v _(j,z)(k)where v_(j,x)(k), v_(j,y)(k), v_(j,z)(k) are wind-speed values projectedinto a given coordinate system at the initial time (k), and a₁, b₁, c₁with j=0, 1, 2, 3, 4 are measurement coefficients, which are given by$\left\{ {\begin{matrix}{{{a_{j} = {\cos \left( \theta_{j} \right)}},}\mspace{79mu}} \\{{b_{j} = {{\sin \left( \theta_{j} \right)}\mspace{14mu} {\cos \left( \phi_{j} \right)}}},} \\{{c_{j} = {{\sin \left( \theta_{j} \right)}\mspace{14mu} {\sin \left( \phi_{j} \right)}}}\;}\end{matrix}\quad} \right.$ where θj, φj, j=0, 1, 2, 3, 4 are,respectively, a zenith and an azimuth of the measurement axis in aspherical coordinate system.
 24. The method according to claim 23,wherein the cost function J at any time (t) is written as:${J(t)} = {{\left( {{\omega (0)} - {\hat{\omega}(0)}} \right)^{T}{P_{0}^{- 1}\left( {{\omega (0)} - {\hat{\omega}(0)}} \right)}} + {\sum\limits_{j = 1}^{t}\; {\left( {{\omega (t)} - {\omega \left( {j - 1} \right)}} \right)^{T}{Q^{- 1}\left( {{\omega (j)} - {\omega \left( {j - 1} \right)}} \right)}}} + {\sum\limits_{j = 1}^{t}\; {{\omega (j)}^{T}C_{s}^{T}R_{s}^{- 1}C_{s}{\omega (j)}}} + {\sum\limits_{j = 1}^{t}\; {\left( {{C_{m}{\omega (j)}} - m_{m}} \right)^{T}{R_{m}^{- 1}\left( {{C_{m}{\omega (j)}} - {m_{m}(j)}} \right)}}}}$in which ω is an ordered vector composed of all components of speed atpoints of the space at which the wind is estimated, {circumflex over(ω)}(0) is estimation of wind speed at the time 0, P₀, Q, R_(s) andR_(m) are weighting matrices, and C_(s), C_(m) are matrices that accountfor the wind speed and the measurement noise.
 25. The method accordingto claim 22, wherein the measurements of amplitude and direction of thewind at measurement points are carried out at a sampling rate of atleast 0.25 Hz.
 26. The method according to claim 22, wherein themeasurements of amplitude and direction of the wind at measurementpoints are carried out at at least two different distances along themeasurement axis.
 27. The method according to claim 22, wherein themeasurements of the amplitude and direction of the wind are taken alongat least three measurement axes.
 28. The method according to claim 22,wherein spatial coherence of wind speed along x, y and z axes in aCartesian coordinate system is estimated with a formula: C_(s)ω ≈ 0with: $C_{s} = \begin{bmatrix}C_{l} \\C_{t} \\C_{v}\end{bmatrix}$ where: C_(l) characterizes variation in wind speed for anestimation domain along the axis x and C_(t) characterizes variation inwind speed for an estimation domain along the axis y and C_(v)characterizes variation in wind speed for an estimation domain along thevertical axis z and the vector ω is an ordered vector composed of allthe components of the wind speed at the points of the space at which thewind is estimated.
 29. The method according to claim 22, wherein thecoherence of wind speed along the x, y and z axes of the Cartesiancoordinate system is estimated under assumptions of: variation in thewind speed is along the longitudinal x axis and a partial derivativedv_(x)/dx is along the longitudinal x axis; wind changes withoutdiscontinuity along the y axis and the partial derivative dv_(x)/dy isalong the y axis; and the wind changes along the z axis are according toa power law, which is given by an equation:$v_{l} = {v_{lr}\left( \frac{z}{z_{r}} \right)}^{\alpha}$ where α is anexponent of a power law, v_(l) is longitudinal wind at an altitude zabove ground, and z_(r) is a reference altitude.
 30. The methodaccording to claim 22, wherein measurements carried out by the lidarsensor are represented using a model defined by:C _(m) ω=m _(m)+∈_(m) with E_(m) describing measurement noise.
 31. Themethod according to claim 22, wherein estimation of amplitudes anddirections of the wind field at a time (t) at all of the estimationpoints which is defined by the following relationship:ω(t)=ω(t−1)+K(y(t)−Cω(t−1)) wherein w(t)=, w(t−1) is, ky(t) is, andCw(t−1) is.
 32. A computer-program product comprising code instructionswhich when executed by a processor of the lidar sensor implement stepsof a method for detecting with a lidar sensor an incident wind fieldaccording to claim
 19. 33. A lidar sensor comprising in codeinstructions of a computer-program according to claim
 32. 34. A windturbine comprising a lidar sensor 2 according to claim 33 within a windturbine.
 35. A wind turbine according to claim 34, wherein the lidarsensor is placed on a nacelle of the wind turbine.
 36. Method forcontrolling and monitoring a wind turbine equipped with a lidar sensor 2and a programmable logic controller, comprising the following steps: i)detecting aberrant values of an incident wind field in a space locatedupstream of a lidar sensor and a step according to claim 19, ii) control(PIL), incorporating the generated control strategy, which controls theangle of the blades 7 or the orientation of a nacelle 3 while notaccounting for the detected aberrant values.